Single-type differential game with a ring-shaped terminal set and a possible breakdown

Key Points

• The optimal strategies are influenced by the geometrical properties of the terminal set, which is ring-shaped and affects the game's dynamics.
• Strategic breakdowns may lead to unexpected shifts in optimal control, necessitating adaptations in responses.
• Assessment using control theory methods demonstrates the complexities within differential games involving a ring-shaped terminal set.
• This work highlights the importance of terminal set shapes in developing strategies; further exploration in different geometric configurations is warranted.